The present invention relates to a method for measuring a gradient index distribution of a rod lens and particularly to a method for measuring a gradient index distribution of a gradient index rod lens by calculating higher-order index distribution coefficients of the rod lens on the basis of measurement of curvature of field. The method according to the invention is a technique particularly useful for evaluation of optical performance of a small-diameter rod lens.
As known commonly, a gradient index rod lens is a lens having a columnar transparent body to which a distribution of refractive index symmetric with respect to the optical axis of the lens is given. The refractive index of the lens is distributed so that the refractive index is high on the optical axis but is reduced continuously toward the periphery of the lens. The gradient index rod lens of this type has been used as a collimator lens or the like in an optical communication system, an optical measurement control system or the like because reduction in size and weight can be achieved. In addition, a lens array constituted by a large number of the gradient index rod lenses of this type arranged regularly in the form of an array has been used as a scanning optical system in a copying machine, a facsimile machine, a printer or the like.
Various methods have been proposed for giving a gradient index distribution to a columnar transparent body (glass rod). The method put into most practical use is an ion exchange method. This is a method in which a glass rod containing high-refractive-index ions is immersed in molten salt containing low-refractive-index ions to disperse the two types of ions into each other to thereby form a distribution of refractive index (gradient index distribution) approximately proportional to the distribution of ion concentrations.
The optical performance of the rod lens of this type mainly depends on the shape of the gradient index distribution. It is therefore necessary to control the distribution for production of the lens. For this reason, the gradient index distribution is required to be measured accurately. In addition, index distribution coefficients are very important as basic data for evaluation of variation in ion exchange and lens design or for system design using such a rod lens.
As a method for obtaining a gradient index distribution of a gradient index rod lens, there has been heretofore used a method of calculating back the gradient index distribution by measuring spherical aberration of a P/4 lens (in which P represents a paraxial period length) (see“Measurement and Analysis of Aberration of Gradient Index Lens”, Optics Vol. 11, No. 6 (December 1982)).
Also in the rod lens, spherical aberration can be obtained by direct measurement of the locus of laser light. That is, because laser light incident on one end surface of a lens to be inspected passes through the lens and exits from the other end surface of the lens, the locus of light rays is obtained by observation of exit light rays. When the measurement is repeated while the position of incidence of light is changed, flux of exit light rays is obtained so that spherical aberration can be obtained. The related-art method is a method in which a light ray equation is solved by a perturbation method in consideration of a gradient index distribution of a gradient index rod lens up to higher-order terms to thereby obtain approximate solutions to parallel light incidence so that spherical aberration of the lens is measured by application of the approximate solutions to thereby obtain index distribution constants.
In the related-art method using the measurement of spherical aberration, it is however necessary that the measurement is repeated while the position of incidence of light is changed in a direction of the radius of the rod lens. Accordingly, it is difficult to measure spherical aberration particularly when the small-diameter rod lens has a diameter not larger than about 1 mm. With the advance of reduction in size of various kinds of optical devices in recent years, the rod lens to be incorporated in each of the optical devices is required to have a further smaller diameter. Accordingly, the index distribution coefficients can be hardly obtained by the related-art method.
In addition, the related-art method needs laser light as a light source. Hence, there is also a problem that the wavelength for measurement is limited to the wavelength of laser light used.